Never seen all of these together

Calculus Level 5

\[ \large \int_0^{\infty} \left( \frac{1}{1 + 4x^2} - \cos(2x) \right) \frac{dx}{x} \]

If the value of the above integral is \( I \). Evaluate \( \displaystyle \lfloor 100 I \rfloor \).

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